On the classification of stationary electro-vacuum black holes

We obtain a classification of stationary, $I^+$--regular, non-degenerate and analytic electro-vacuum space-times in terms of Weinstein solutions. In particular, for connected horizons, we prove uniqueness of the Kerr-Newman black holes

Elastic shocks in relativistic rigid rods and balls

We study the free boundary problem for the "hard phase" material introduced by Christodoulou, both for rods in (1+1)-dimensional Minkowski spacetime and for spherically symmetric balls in (3+1)-dimensional Minkowski spacetime. Unlike Christodoulou, we do not consider a "soft phase", and so we regard this material as an elastic medium, capable of both compression and stretching. We prove that shocks must be null hypersurfaces, and derive the conditions to be satisfied at a free boundary. We solve the equations of motion of the rods explicitly, and we prove existence of solutions to the equations of motion of the spherically symmetric balls for an arbitrarily long (but finite) time, given initial conditions sufficiently close to those for the relaxed ball at rest. In both cases we find that the solutions contain shocks if and only if the pressure or its time derivative do not vanish at the free boundary initially. These shocks interact with the free boundary, causing it to lose regularity.Comment: 22 pages, 3 figures; v2: small changes, matches final published version; v3: typos in the references fixe

A Geant4 based engineering tool for Fresnel lenses

Geant4 is a Monte Carlo radiation transport toolkit that is becoming a tool of generalized application in areas such as high-energy physics, nuclear physics, astroparticle physics, or medical physics. Geant4 provides an optical physics process category, allowing the simulation of the production and propagation of light. Its capabilities are well tailored for the simulation of optics systems namely in cosmic-rays experiments based in the detection of Cherenkov and fluorescence light. The use of Geant4 as an engineering tool for the optics design and simulation of Fresnel lens systems is discussed through a specific example.Comment: 4 pages, 6 figures, Proceedings of the 30th ICRC, International Cosmic Ray Conference 2007, M\'erida, M\'exico, 3-11 July 200

Homogeneous cosmologies from the quasi-Maxwell formalism

We show how to use the quasi-Maxwell formalism to obtain solutions of Einstein's field equations corresponding to homogeneous cosmologies - namely Einstein's universe, Godel's universe and the Ozsvath-Farnsworth-Kerr class I solutions - written in frames for which the associated observers are stationary.Comment: 15 pages, references adde

Asymptotic expansions, LL-values and a new Quantum Modular Form

In 2010 Zagier introduced the notion of a quantum modular form. One of his first examples was the "strange" function $F(q)$ of Kontsevich. Here we produce a new example of a quantum modular form by making use of some of Ramanujan's mock theta functions. Using these functions and their transformation behaviour, we also compute asymptotic expansions similar to expansions of $F(q)$.Comment: 7 page